The Fermi edge singularity (FES) is a prominent manifestation of the Coulomb interaction. It can be observed in a controllable way by studying the transport through a quantum dot (QD), which is electrostatically coupled to the leads. In this paper we study how FES affects higher order tunneling processes (cotunneling). To address this problem we use the bosonic description of the electrons in the leads, which naturally accounts for the Coulomb interaction. We report the multiscale dependence of the current through the QD on the energy of the QD level and on the bias between the leads obtained for the limit of large and small bias. The new universal powers are determined by the scattering phases due to the interaction of electrons in the leads with the charge on the QD.